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Solution
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Solution provided by AtoZmath.com
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Functions - Find Range of f:A->B calculator
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1. Find Range of `f:A->B`
 1. `f(x)=5x+2` where `A={1<=x<5}`
2. `f(x)=|2x+1|` where `A={x in Z}`
3. `f(x)=sqrt(x)` where `A={1,4,16,36}`
4. `f(x)=(-2)^x` where `A={x in N}`
5. `f(x)=(x^2+1)/(x+1)` where `A={-2,0,2}`
2. Composite functions and Evaluating functions
1. `f(x)=2x+1`, `g(x)=x+5`. Find `fog(x)`, also evaluate at `x=2`
2. `f(x)=x+3`, `g(x)=x^2`. Find `gof(x)`
3. `f(x)=3x+1`, `g(x)=-x^2+5`. Find `gof(x)`
4. `f(x)=4x+1`, `g(x)=2x-3`. Find `gof(x)`, also evaluate at `x=2`
5. `fog(x)=(x+2)/(3x), f(x)=x-2`. Find g(2).
6. `gof(x)=1/x^2, f(x)=2+x^2`. Find g(x).
3. Find value
1. `f(x)=x(x+1)(2x+1)`. Find `f(x)-f(x-1)`
2. `f(x)=1/x`. Find `f(x+1)-f(x-1)`
3. `f(x)=x^2-x`. Find `f(x+1)-f(x)`
4. `f(x)=x^2-2^x`. Find `f(2)-f(0)`
5. `f(x)=(x^2+1)/(x^3-x+1)`. Find `f(1)-f(0)`
4. Verifying if two functions are inverses of each other
1. `f(x)=x+3,g(x)=x-3`
2. `f(x)=4x-3,g(x)=(x+3)/4`
3. `f(x)=x/(x-1),g(x)=(2x)/(2x-1)`
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Example1. Find Range of `f:A->B`
`f(x)=5x+2` where `A={1<=x<5}`
Solution:
Here `A={1<=x<5}`
`:. D_f={1,2,3,4}`
Here `f(x)=5x+2`
`f(1)``=5*1+2`
`=5+2`
`=7`
`f(2)``=5*2+2`
`=10+2`
`=12`
`f(3)``=5*3+2`
`=15+2`
`=17`
`f(4)``=5*4+2`
`=20+2`
`=22`
`:.R_f={7,12,17,22}`
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Input functions
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| Sr No. |
Function |
Input value |
| 1. |
`x^3` |
x^3 |
| 2. |
`sqrt(x)` |
sqrt(x) |
| 3. |
`root(3)(x)`
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root(3,x)
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| 4. |
sin(x) |
sin(x) |
| 5. |
cos(x) |
cos(x) |
| 6. |
tan(x) |
tan(x) |
| 7. |
sec(x) |
sec(x) |
| 8. |
cosec(x) |
csc(x) |
| 9. |
cot(x) |
cot(x) |
| 10. |
`sin^(-1)(x)` |
asin(x) |
| 11. |
`cos^(-1)(x)` |
acos(x) |
| 12. |
`tan^(-1)(x)` |
atan(x) |
| 13. |
`sin^2(x)` |
sin^2(x) |
| 14. |
`log_y(x)` |
log(y,x) |
| 15. |
`log_10(x)` |
log(x) |
| 16. |
`log_e(x)` |
ln(x) |
| 17. |
`e^x` |
exp(x) or e^x |
| 18. |
`e^(2x)` |
exp(2x) or e^(2x) |
| 19. |
`oo` |
inf |
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